Geodesic
Regularity of solutions to Dirichlet boundary value problem in domains on a manifold
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2016), pp. 44-49

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The regularity of solutions to the Dirchlet boundary value problem is studied for elliptic differential operators of order $2m$ defined on subdomains of a manifold. Relationships between the smoothness of the right hand side, the boundary, and the solutions are obtained. 
@article{VMUMM_2016_5_a7,
     author = {I. V. Tsylin},
     title = {Regularity of solutions to {Dirichlet} boundary value problem in domains on a manifold},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {44--49},
     publisher = {mathdoc},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_5_a7/}
}
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I. V. Tsylin. Regularity of solutions to Dirichlet boundary value problem in domains on a manifold. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2016), pp. 44-49. http://geodesic.mathdoc.fr/item/VMUMM_2016_5_a7/